Actual source code: schurm.c
1: #include <../src/ksp/ksp/utils/schurm/schurm.h>
3: const char *const MatSchurComplementAinvTypes[] = {"DIAG","LUMP","BLOCKDIAG","MatSchurComplementAinvType","MAT_SCHUR_COMPLEMENT_AINV_",NULL};
5: PetscErrorCode MatCreateVecs_SchurComplement(Mat N,Vec *right,Vec *left)
6: {
7: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
8: PetscErrorCode ierr;
11: if (Na->D) {
12: MatCreateVecs(Na->D,right,left);
13: return(0);
14: }
15: if (right) {
16: MatCreateVecs(Na->B,right,NULL);
17: }
18: if (left) {
19: MatCreateVecs(Na->C,NULL,left);
20: }
21: return(0);
22: }
24: PetscErrorCode MatView_SchurComplement(Mat N,PetscViewer viewer)
25: {
26: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
27: PetscErrorCode ierr;
30: PetscViewerASCIIPrintf(viewer,"Schur complement A11 - A10 inv(A00) A01\n");
31: if (Na->D) {
32: PetscViewerASCIIPrintf(viewer,"A11\n");
33: PetscViewerASCIIPushTab(viewer);
34: MatView(Na->D,viewer);
35: PetscViewerASCIIPopTab(viewer);
36: } else {
37: PetscViewerASCIIPrintf(viewer,"A11 = 0\n");
38: }
39: PetscViewerASCIIPrintf(viewer,"A10\n");
40: PetscViewerASCIIPushTab(viewer);
41: MatView(Na->C,viewer);
42: PetscViewerASCIIPopTab(viewer);
43: PetscViewerASCIIPrintf(viewer,"KSP of A00\n");
44: PetscViewerASCIIPushTab(viewer);
45: KSPView(Na->ksp,viewer);
46: PetscViewerASCIIPopTab(viewer);
47: PetscViewerASCIIPrintf(viewer,"A01\n");
48: PetscViewerASCIIPushTab(viewer);
49: MatView(Na->B,viewer);
50: PetscViewerASCIIPopTab(viewer);
51: return(0);
52: }
54: /*
55: A11^T - A01^T ksptrans(A00,Ap00) A10^T
56: */
57: PetscErrorCode MatMultTranspose_SchurComplement(Mat N,Vec x,Vec y)
58: {
59: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
60: PetscErrorCode ierr;
63: if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
64: if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
65: MatMultTranspose(Na->C,x,Na->work1);
66: KSPSolveTranspose(Na->ksp,Na->work1,Na->work2);
67: MatMultTranspose(Na->B,Na->work2,y);
68: VecScale(y,-1.0);
69: if (Na->D) {
70: MatMultTransposeAdd(Na->D,x,y,y);
71: }
72: return(0);
73: }
75: /*
76: A11 - A10 ksp(A00,Ap00) A01
77: */
78: PetscErrorCode MatMult_SchurComplement(Mat N,Vec x,Vec y)
79: {
80: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
81: PetscErrorCode ierr;
84: if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
85: if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
86: MatMult(Na->B,x,Na->work1);
87: KSPSolve(Na->ksp,Na->work1,Na->work2);
88: MatMult(Na->C,Na->work2,y);
89: VecScale(y,-1.0);
90: if (Na->D) {
91: MatMultAdd(Na->D,x,y,y);
92: }
93: return(0);
94: }
96: /*
97: A11 - A10 ksp(A00,Ap00) A01
98: */
99: PetscErrorCode MatMultAdd_SchurComplement(Mat N,Vec x,Vec y,Vec z)
100: {
101: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
102: PetscErrorCode ierr;
105: if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
106: if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
107: MatMult(Na->B,x,Na->work1);
108: KSPSolve(Na->ksp,Na->work1,Na->work2);
109: if (y == z) {
110: VecScale(Na->work2,-1.0);
111: MatMultAdd(Na->C,Na->work2,z,z);
112: } else {
113: MatMult(Na->C,Na->work2,z);
114: VecAYPX(z,-1.0,y);
115: }
116: if (Na->D) {
117: MatMultAdd(Na->D,x,z,z);
118: }
119: return(0);
120: }
122: PetscErrorCode MatSetFromOptions_SchurComplement(PetscOptionItems *PetscOptionsObject,Mat N)
123: {
124: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
125: PetscErrorCode ierr;
128: PetscOptionsHead(PetscOptionsObject,"MatSchurComplementOptions");
129: Na->ainvtype = MAT_SCHUR_COMPLEMENT_AINV_DIAG;
130: PetscOptionsEnum("-mat_schur_complement_ainv_type","Type of approximation for inv(A00) used when assembling Sp = A11 - A10 inv(A00) A01","MatSchurComplementSetAinvType",MatSchurComplementAinvTypes,(PetscEnum)Na->ainvtype,(PetscEnum*)&Na->ainvtype,NULL);
131: PetscOptionsTail();
132: KSPSetFromOptions(Na->ksp);
133: return(0);
134: }
136: PetscErrorCode MatDestroy_SchurComplement(Mat N)
137: {
138: Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
139: PetscErrorCode ierr;
142: MatDestroy(&Na->A);
143: MatDestroy(&Na->Ap);
144: MatDestroy(&Na->B);
145: MatDestroy(&Na->C);
146: MatDestroy(&Na->D);
147: VecDestroy(&Na->work1);
148: VecDestroy(&Na->work2);
149: KSPDestroy(&Na->ksp);
150: PetscFree(N->data);
151: return(0);
152: }
154: /*@
155: MatCreateSchurComplement - Creates a new matrix object that behaves like the Schur complement of a matrix
157: Collective on A00
159: Input Parameters:
160: + A00,A01,A10,A11 - the four parts of the original matrix A = [A00 A01; A10 A11] (A11 is optional)
161: - Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}
163: Output Parameter:
164: . S - the matrix that the Schur complement S = A11 - A10 ksp(A00,Ap00) A01
166: Level: intermediate
168: Notes:
169: The Schur complement is NOT actually formed! Rather, this
170: object performs the matrix-vector product by using formula S = A11 - A10 A^{-1} A01
171: for Schur complement S and a KSP solver to approximate the action of A^{-1}.
173: All four matrices must have the same MPI communicator.
175: A00 and A11 must be square matrices.
177: MatGetSchurComplement() takes as arguments the index sets for the submatrices and returns both the virtual Schur complement (what this returns) plus
178: a sparse approximation to the true Schur complement (useful for building a preconditioner for the Schur complement).
180: MatSchurComplementGetPmat() can be called on the output of this function to generate an explicit approximation to the Schur complement.
182: Developer Notes:
183: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
184: remove redundancy and be clearer and simpler.
186: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatGetSchurComplement(),
187: MatSchurComplementGetPmat()
189: @*/
190: PetscErrorCode MatCreateSchurComplement(Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11,Mat *S)
191: {
195: KSPInitializePackage();
196: MatCreate(PetscObjectComm((PetscObject)A00),S);
197: MatSetType(*S,MATSCHURCOMPLEMENT);
198: MatSchurComplementSetSubMatrices(*S,A00,Ap00,A01,A10,A11);
199: return(0);
200: }
202: /*@
203: MatSchurComplementSetSubMatrices - Sets the matrices that define the Schur complement
205: Collective on S
207: Input Parameters:
208: + S - matrix obtained with MatCreateSchurComplement (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
209: . A00,A01,A10,A11 - the four parts of A = [A00 A01; A10 A11] (A11 is optional)
210: - Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.
212: Level: intermediate
214: Notes:
215: The Schur complement is NOT actually formed! Rather, this
216: object performs the matrix-vector product by using formula S = A11 - A10 A^{-1} A01
217: for Schur complement S and a KSP solver to approximate the action of A^{-1}.
219: All four matrices must have the same MPI communicator.
221: A00 and A11 must be square matrices.
223: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatCreateSchurComplement(), MatGetSchurComplement()
225: @*/
226: PetscErrorCode MatSchurComplementSetSubMatrices(Mat S,Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11)
227: {
228: PetscErrorCode ierr;
229: Mat_SchurComplement *Na = (Mat_SchurComplement*)S->data;
230: PetscBool isschur;
233: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
234: if (!isschur) return(0);
235: if (S->assembled) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Use MatSchurComplementUpdateSubMatrices() for already used matrix");
243: if (A00->rmap->n != A00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local columns %D",A00->rmap->n,A00->cmap->n);
244: if (A00->rmap->n != Ap00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local rows of Ap00 %D",A00->rmap->n,Ap00->rmap->n);
245: if (Ap00->rmap->n != Ap00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of Ap00 %D do not equal local columns %D",Ap00->rmap->n,Ap00->cmap->n);
246: if (A00->cmap->n != A01->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A00 %D do not equal local rows of A01 %D",A00->cmap->n,A01->rmap->n);
247: if (A10->cmap->n != A00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A10 %D do not equal local rows of A00 %D",A10->cmap->n,A00->rmap->n);
248: if (A11) {
251: if (A10->rmap->n != A11->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A10 %D do not equal local rows A11 %D",A10->rmap->n,A11->rmap->n);
252: }
254: MatSetSizes(S,A10->rmap->n,A01->cmap->n,A10->rmap->N,A01->cmap->N);
255: PetscObjectReference((PetscObject)A00);
256: PetscObjectReference((PetscObject)Ap00);
257: PetscObjectReference((PetscObject)A01);
258: PetscObjectReference((PetscObject)A10);
259: Na->A = A00;
260: Na->Ap = Ap00;
261: Na->B = A01;
262: Na->C = A10;
263: Na->D = A11;
264: if (A11) {
265: PetscObjectReference((PetscObject)A11);
266: }
267: MatSetUp(S);
268: KSPSetOperators(Na->ksp,A00,Ap00);
269: S->assembled = PETSC_TRUE;
270: return(0);
271: }
273: /*@
274: MatSchurComplementGetKSP - Gets the KSP object that is used to invert A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01
276: Not Collective
278: Input Parameter:
279: . S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
281: Output Parameter:
282: . ksp - the linear solver object
284: Options Database:
285: . -fieldsplit_<splitname_0>_XXX sets KSP and PC options for the 0-split solver inside the Schur complement used in PCFieldSplit; default <splitname_0> is 0.
287: Level: intermediate
289: .seealso: MatSchurComplementSetKSP(), MatCreateSchurComplement(), MatCreateNormal(), MatMult(), MatCreate()
290: @*/
291: PetscErrorCode MatSchurComplementGetKSP(Mat S, KSP *ksp)
292: {
293: Mat_SchurComplement *Na;
294: PetscBool isschur;
295: PetscErrorCode ierr;
299: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
300: if (!isschur) SETERRQ1(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONG,"Not for type %s",((PetscObject)S)->type_name);
302: Na = (Mat_SchurComplement*) S->data;
303: *ksp = Na->ksp;
304: return(0);
305: }
307: /*@
308: MatSchurComplementSetKSP - Sets the KSP object that is used to invert A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01
310: Not Collective
312: Input Parameters:
313: + S - matrix created with MatCreateSchurComplement()
314: - ksp - the linear solver object
316: Level: developer
318: Developer Notes:
319: This is used in PCFieldSplit to reuse the 0-split KSP to implement ksp(A00,Ap00) in S.
320: The KSP operators are overwritten with A00 and Ap00 currently set in S.
322: .seealso: MatSchurComplementGetKSP(), MatCreateSchurComplement(), MatCreateNormal(), MatMult(), MatCreate(), MATSCHURCOMPLEMENT
323: @*/
324: PetscErrorCode MatSchurComplementSetKSP(Mat S, KSP ksp)
325: {
326: Mat_SchurComplement *Na;
327: PetscErrorCode ierr;
328: PetscBool isschur;
332: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
333: if (!isschur) return(0);
335: Na = (Mat_SchurComplement*) S->data;
336: PetscObjectReference((PetscObject)ksp);
337: KSPDestroy(&Na->ksp);
338: Na->ksp = ksp;
339: KSPSetOperators(Na->ksp, Na->A, Na->Ap);
340: return(0);
341: }
343: /*@
344: MatSchurComplementUpdateSubMatrices - Updates the Schur complement matrix object with new submatrices
346: Collective on S
348: Input Parameters:
349: + S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
350: . A00,A01,A10,A11 - the four parts of A = [A00 A01; A10 A11] (A11 is optional)
351: - Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.
353: Level: intermediate
355: Notes:
356: All four matrices must have the same MPI communicator
358: A00 and A11 must be square matrices
360: All of the matrices provided must have the same sizes as was used with MatCreateSchurComplement() or MatSchurComplementSetSubMatrices()
361: though they need not be the same matrices.
363: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatCreateSchurComplement()
365: @*/
366: PetscErrorCode MatSchurComplementUpdateSubMatrices(Mat S,Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11)
367: {
368: PetscErrorCode ierr;
369: Mat_SchurComplement *Na = (Mat_SchurComplement*)S->data;
370: PetscBool isschur;
374: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
375: if (!isschur) return(0);
376: if (!S->assembled) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Use MatSchurComplementSetSubMatrices() for a new matrix");
384: if (A00->rmap->n != A00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local columns %D",A00->rmap->n,A00->cmap->n);
385: if (A00->rmap->n != Ap00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local rows of Ap00 %D",A00->rmap->n,Ap00->rmap->n);
386: if (Ap00->rmap->n != Ap00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of Ap00 %D do not equal local columns %D",Ap00->rmap->n,Ap00->cmap->n);
387: if (A00->cmap->n != A01->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A00 %D do not equal local rows of A01 %D",A00->cmap->n,A01->rmap->n);
388: if (A10->cmap->n != A00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A10 %D do not equal local rows of A00 %D",A10->cmap->n,A00->rmap->n);
389: if (A11) {
392: if (A10->rmap->n != A11->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A10 %D do not equal local rows A11 %D",A10->rmap->n,A11->rmap->n);
393: }
395: PetscObjectReference((PetscObject)A00);
396: PetscObjectReference((PetscObject)Ap00);
397: PetscObjectReference((PetscObject)A01);
398: PetscObjectReference((PetscObject)A10);
399: if (A11) {
400: PetscObjectReference((PetscObject)A11);
401: }
403: MatDestroy(&Na->A);
404: MatDestroy(&Na->Ap);
405: MatDestroy(&Na->B);
406: MatDestroy(&Na->C);
407: MatDestroy(&Na->D);
409: Na->A = A00;
410: Na->Ap = Ap00;
411: Na->B = A01;
412: Na->C = A10;
413: Na->D = A11;
415: KSPSetOperators(Na->ksp,A00,Ap00);
416: return(0);
417: }
419: /*@C
420: MatSchurComplementGetSubMatrices - Get the individual submatrices in the Schur complement
422: Collective on S
424: Input Parameter:
425: . S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
427: Output Parameters:
428: + A00 - the upper-left block of the original matrix A = [A00 A01; A10 A11]
429: . Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}
430: . A01 - the upper-right block of the original matrix A = [A00 A01; A10 A11]
431: . A10 - the lower-left block of the original matrix A = [A00 A01; A10 A11]
432: - A11 - (optional) the lower-right block of the original matrix A = [A00 A01; A10 A11]
434: Note: A11 is optional, and thus can be NULL. The submatrices are not increfed before they are returned and should not be modified or destroyed.
436: Level: intermediate
438: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatCreateSchurComplement(), MatSchurComplementUpdateSubMatrices()
439: @*/
440: PetscErrorCode MatSchurComplementGetSubMatrices(Mat S,Mat *A00,Mat *Ap00,Mat *A01,Mat *A10,Mat *A11)
441: {
442: Mat_SchurComplement *Na = (Mat_SchurComplement*) S->data;
443: PetscErrorCode ierr;
444: PetscBool flg;
448: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&flg);
449: if (!flg) SETERRQ1(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONG,"Not for type %s",((PetscObject)S)->type_name);
450: if (A00) *A00 = Na->A;
451: if (Ap00) *Ap00 = Na->Ap;
452: if (A01) *A01 = Na->B;
453: if (A10) *A10 = Na->C;
454: if (A11) *A11 = Na->D;
455: return(0);
456: }
458: #include <petsc/private/kspimpl.h>
460: /*@
461: MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly
463: Collective on M
465: Input Parameter:
466: . M - the matrix obtained with MatCreateSchurComplement()
468: Output Parameter:
469: . S - the Schur complement matrix
471: Note: This can be expensive, so it is mainly for testing
473: Level: advanced
475: .seealso: MatCreateSchurComplement(), MatSchurComplementUpdate()
476: @*/
477: PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat A, Mat *S)
478: {
479: Mat B, C, D, Bd, AinvBd;
480: KSP ksp;
481: PetscInt n,N,m,M;
485: MatSchurComplementGetSubMatrices(A, NULL, NULL, &B, &C, &D);
486: MatSchurComplementGetKSP(A, &ksp);
487: KSPSetUp(ksp);
488: MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &Bd);
489: MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);
490: KSPMatSolve(ksp, Bd, AinvBd);
491: MatDestroy(&Bd);
492: MatChop(AinvBd, PETSC_SMALL);
493: if (D) {
494: MatGetLocalSize(D, &m, &n);
495: MatGetSize(D, &M, &N);
496: MatCreateDense(PetscObjectComm((PetscObject)A), m, n, M, N, NULL, S);
497: }
498: MatMatMult(C, AinvBd, D ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX, PETSC_DEFAULT, S);
499: MatDestroy(&AinvBd);
500: if (D) {
501: MatAXPY(*S, -1.0, D, DIFFERENT_NONZERO_PATTERN);
502: }
503: MatConvert(*S, MATAIJ, MAT_INPLACE_MATRIX, S);
504: MatScale(*S, -1.0);
505: return(0);
506: }
508: /* Developer Notes:
509: This should be implemented with a MatCreate_SchurComplement() as that is the standard design for new Mat classes. */
510: PetscErrorCode MatGetSchurComplement_Basic(Mat mat,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *newmat,MatSchurComplementAinvType ainvtype, MatReuse preuse,Mat *newpmat)
511: {
513: Mat A=NULL,Ap=NULL,B=NULL,C=NULL,D=NULL;
514: MatReuse reuse;
526: if (mreuse == MAT_IGNORE_MATRIX && preuse == MAT_IGNORE_MATRIX) return(0);
530: if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
532: reuse = MAT_INITIAL_MATRIX;
533: if (mreuse == MAT_REUSE_MATRIX) {
534: MatSchurComplementGetSubMatrices(*newmat,&A,&Ap,&B,&C,&D);
535: if (!A || !Ap || !B || !C) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Attempting to reuse matrix but Schur complement matrices unset");
536: if (A != Ap) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Preconditioning matrix does not match operator");
537: MatDestroy(&Ap); /* get rid of extra reference */
538: reuse = MAT_REUSE_MATRIX;
539: }
540: MatCreateSubMatrix(mat,isrow0,iscol0,reuse,&A);
541: MatCreateSubMatrix(mat,isrow0,iscol1,reuse,&B);
542: MatCreateSubMatrix(mat,isrow1,iscol0,reuse,&C);
543: MatCreateSubMatrix(mat,isrow1,iscol1,reuse,&D);
544: switch (mreuse) {
545: case MAT_INITIAL_MATRIX:
546: MatCreateSchurComplement(A,A,B,C,D,newmat);
547: break;
548: case MAT_REUSE_MATRIX:
549: MatSchurComplementUpdateSubMatrices(*newmat,A,A,B,C,D);
550: break;
551: default:
552: if (mreuse != MAT_IGNORE_MATRIX) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Unrecognized value of mreuse %d",(int)mreuse);
553: }
554: if (preuse != MAT_IGNORE_MATRIX) {
555: MatCreateSchurComplementPmat(A,B,C,D,ainvtype,preuse,newpmat);
556: }
557: MatDestroy(&A);
558: MatDestroy(&B);
559: MatDestroy(&C);
560: MatDestroy(&D);
561: return(0);
562: }
564: /*@
565: MatGetSchurComplement - Obtain the Schur complement from eliminating part of the matrix in another part.
567: Collective on A
569: Input Parameters:
570: + A - matrix in which the complement is to be taken
571: . isrow0 - rows to eliminate
572: . iscol0 - columns to eliminate, (isrow0,iscol0) should be square and nonsingular
573: . isrow1 - rows in which the Schur complement is formed
574: . iscol1 - columns in which the Schur complement is formed
575: . mreuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in S
576: . ainvtype - the type of approximation used for the inverse of the (0,0) block used in forming Sp:
577: MAT_SCHUR_COMPLEMENT_AINV_DIAG, MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG, or MAT_SCHUR_COMPLEMENT_AINV_LUMP
578: - preuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in Sp
580: Output Parameters:
581: + S - exact Schur complement, often of type MATSCHURCOMPLEMENT which is difficult to use for preconditioning
582: - Sp - approximate Schur complement from which a preconditioner can be built
584: Note:
585: Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
586: application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
587: the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
588: before forming inv(diag(A00)).
590: Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row
591: and column index sets. In that case, the user should call PetscObjectComposeFunction() on the *S matrix and pass mreuse of MAT_REUSE_MATRIX to set
592: "MatGetSchurComplement_C" to their function. If their function needs to fall back to the default implementation, it
593: should call MatGetSchurComplement_Basic().
595: MatCreateSchurComplement() takes as arguments the four submatrices and returns the virtual Schur complement (what this returns in S).
597: MatSchurComplementGetPmat() takes the virtual Schur complement and returns an explicit approximate Schur complement (what this returns in Sp).
599: In other words calling MatCreateSchurComplement() followed by MatSchurComplementGetPmat() produces the same output as this function but with slightly different
600: inputs. The actually submatrices of the original block matrix instead of index sets to the submatrices.
602: Developer Notes:
603: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
604: remove redundancy and be clearer and simpler.
606: Level: advanced
608: .seealso: MatCreateSubMatrix(), PCFIELDSPLIT, MatCreateSchurComplement(), MatSchurComplementAinvType
609: @*/
610: PetscErrorCode MatGetSchurComplement(Mat A,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *S,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Sp)
611: {
612: PetscErrorCode ierr,(*f)(Mat,IS,IS,IS,IS,MatReuse,Mat*,MatReuse,Mat*) = NULL;
626: if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
627: f = NULL;
628: if (mreuse == MAT_REUSE_MATRIX) { /* This is the only situation, in which we can demand that the user pass a non-NULL pointer to non-garbage in S. */
629: PetscObjectQueryFunction((PetscObject)*S,"MatGetSchurComplement_C",&f);
630: }
631: if (f) {
632: (*f)(A,isrow0,iscol0,isrow1,iscol1,mreuse,S,preuse,Sp);
633: } else {
634: MatGetSchurComplement_Basic(A,isrow0,iscol0,isrow1,iscol1,mreuse,S,ainvtype,preuse,Sp);
635: }
636: return(0);
637: }
639: /*@
640: MatSchurComplementSetAinvType - set the type of approximation used for the inverse of the (0,0) block used in forming Sp in MatSchurComplementGetPmat()
642: Not collective.
644: Input Parameters:
645: + S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
646: - ainvtype - type of approximation used to form A00inv from A00 when assembling Sp = A11 - A10 A00inv A01:
647: MAT_SCHUR_COMPLEMENT_AINV_DIAG, MAT_SCHUR_COMPLEMENT_AINV_LUMP, or MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG
649: Options database:
650: -mat_schur_complement_ainv_type diag | lump | blockdiag
652: Note:
653: Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
654: application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
655: the (0,0) block A00 in place of A00^{-1}. This rarely produces a scalable algorithm. Optionally, A00 can be lumped
656: before forming inv(diag(A00)).
658: Level: advanced
660: .seealso: MatSchurComplementAinvType, MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementGetAinvType()
661: @*/
662: PetscErrorCode MatSchurComplementSetAinvType(Mat S,MatSchurComplementAinvType ainvtype)
663: {
664: PetscErrorCode ierr;
665: PetscBool isschur;
666: Mat_SchurComplement *schur;
670: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
671: if (!isschur) return(0);
673: schur = (Mat_SchurComplement*)S->data;
674: if (ainvtype != MAT_SCHUR_COMPLEMENT_AINV_DIAG && ainvtype != MAT_SCHUR_COMPLEMENT_AINV_LUMP && ainvtype != MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown MatSchurComplementAinvType: %d",(int)ainvtype);
675: schur->ainvtype = ainvtype;
676: return(0);
677: }
679: /*@
680: MatSchurComplementGetAinvType - get the type of approximation for the inverse of the (0,0) block used in forming Sp in MatSchurComplementGetPmat()
682: Not collective.
684: Input Parameter:
685: . S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
687: Output Parameter:
688: . ainvtype - type of approximation used to form A00inv from A00 when assembling Sp = A11 - A10 A00inv A01:
689: MAT_SCHUR_COMPLEMENT_AINV_DIAG, MAT_SCHUR_COMPLEMENT_AINV_LUMP, or MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG
691: Note:
692: Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
693: application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
694: the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
695: before forming inv(diag(A00)).
697: Level: advanced
699: .seealso: MatSchurComplementAinvType, MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementSetAinvType()
700: @*/
701: PetscErrorCode MatSchurComplementGetAinvType(Mat S,MatSchurComplementAinvType *ainvtype)
702: {
703: PetscErrorCode ierr;
704: PetscBool isschur;
705: Mat_SchurComplement *schur;
709: PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&isschur);
710: if (!isschur) SETERRQ1(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONG,"Not for type %s",((PetscObject)S)->type_name);
711: schur = (Mat_SchurComplement*)S->data;
712: if (ainvtype) *ainvtype = schur->ainvtype;
713: return(0);
714: }
716: /*@
717: MatCreateSchurComplementPmat - create a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01
719: Collective on A00
721: Input Parameters:
722: + A00 - the upper-left part of the original matrix A = [A00 A01; A10 A11]
723: . A01 - (optional) the upper-right part of the original matrix A = [A00 A01; A10 A11]
724: . A10 - (optional) the lower-left part of the original matrix A = [A00 A01; A10 A11]
725: . A11 - (optional) the lower-right part of the original matrix A = [A00 A01; A10 A11]
726: . ainvtype - type of approximation for inv(A00) used when forming Sp = A11 - A10 inv(A00) A01
727: - preuse - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp
729: Output Parameter:
730: - Spmat - approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01
732: Note:
733: Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
734: application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
735: the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
736: before forming inv(diag(A00)).
738: Level: advanced
740: .seealso: MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType
741: @*/
742: PetscErrorCode MatCreateSchurComplementPmat(Mat A00,Mat A01,Mat A10,Mat A11,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Spmat)
743: {
745: PetscInt N00;
748: /* Use an appropriate approximate inverse of A00 to form A11 - A10 inv(diag(A00)) A01; a NULL A01, A10 or A11 indicates a zero matrix. */
749: /* TODO: Perhaps should create an appropriately-sized zero matrix of the same type as A00? */
750: if ((!A01 || !A10) & !A11) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot assemble Spmat: A01, A10 and A11 are all NULL.");
752: if (preuse == MAT_IGNORE_MATRIX) return(0);
754: /* A zero size A00 or empty A01 or A10 imply S = A11. */
755: MatGetSize(A00,&N00,NULL);
756: if (!A01 || !A10 || !N00) {
757: if (preuse == MAT_INITIAL_MATRIX) {
758: MatDuplicate(A11,MAT_COPY_VALUES,Spmat);
759: } else { /* MAT_REUSE_MATRIX */
760: /* TODO: when can we pass SAME_NONZERO_PATTERN? */
761: MatCopy(A11,*Spmat,DIFFERENT_NONZERO_PATTERN);
762: }
763: } else {
764: Mat AdB;
765: Vec diag;
767: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP || ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
768: MatDuplicate(A01,MAT_COPY_VALUES,&AdB);
769: MatCreateVecs(A00,&diag,NULL);
770: if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP) {
771: MatGetRowSum(A00,diag);
772: } else {
773: MatGetDiagonal(A00,diag);
774: }
775: VecReciprocal(diag);
776: MatDiagonalScale(AdB,diag,NULL);
777: VecDestroy(&diag);
778: } else if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG) {
779: Mat A00_inv;
780: MatType type;
781: MPI_Comm comm;
783: PetscObjectGetComm((PetscObject)A00,&comm);
784: MatGetType(A00,&type);
785: MatCreate(comm,&A00_inv);
786: MatSetType(A00_inv,type);
787: MatInvertBlockDiagonalMat(A00,A00_inv);
788: MatMatMult(A00_inv,A01,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AdB);
789: MatDestroy(&A00_inv);
790: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown MatSchurComplementAinvType: %D", ainvtype);
791: /* Cannot really reuse Spmat in MatMatMult() because of MatAYPX() -->
792: MatAXPY() --> MatHeaderReplace() --> MatDestroy_XXX_MatMatMult() */
793: MatDestroy(Spmat);
794: MatMatMult(A10,AdB,MAT_INITIAL_MATRIX,PETSC_DEFAULT,Spmat);
795: if (!A11) {
796: MatScale(*Spmat,-1.0);
797: } else {
798: /* TODO: when can we pass SAME_NONZERO_PATTERN? */
799: MatAYPX(*Spmat,-1,A11,DIFFERENT_NONZERO_PATTERN);
800: }
801: MatDestroy(&AdB);
802: }
803: return(0);
804: }
806: PetscErrorCode MatSchurComplementGetPmat_Basic(Mat S,MatReuse preuse,Mat *Spmat)
807: {
808: Mat A,B,C,D;
809: Mat_SchurComplement *schur = (Mat_SchurComplement *)S->data;
810: PetscErrorCode ierr;
813: if (preuse == MAT_IGNORE_MATRIX) return(0);
814: MatSchurComplementGetSubMatrices(S,&A,NULL,&B,&C,&D);
815: if (!A) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Schur complement component matrices unset");
816: MatCreateSchurComplementPmat(A,B,C,D,schur->ainvtype,preuse,Spmat);
817: return(0);
818: }
820: /*@
821: MatSchurComplementGetPmat - Obtain a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01
823: Collective on S
825: Input Parameters:
826: + S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
827: - preuse - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp
829: Output Parameter:
830: - Sp - approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01
832: Note:
833: Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
834: application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
835: the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
836: before forming inv(diag(A00)).
838: Sometimes users would like to provide problem-specific data in the Schur complement, usually only
839: for special row and column index sets. In that case, the user should call PetscObjectComposeFunction() to set
840: "MatSchurComplementGetPmat_C" to their function. If their function needs to fall back to the default implementation,
841: it should call MatSchurComplementGetPmat_Basic().
843: Developer Notes:
844: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
845: remove redundancy and be clearer and simpler.
847: Level: advanced
849: .seealso: MatCreateSubMatrix(), PCFIELDSPLIT, MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementSetAinvType()
850: @*/
851: PetscErrorCode MatSchurComplementGetPmat(Mat S,MatReuse preuse,Mat *Sp)
852: {
853: PetscErrorCode ierr,(*f)(Mat,MatReuse,Mat*);
861: if (S->factortype) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
863: PetscObjectQueryFunction((PetscObject)S,"MatSchurComplementGetPmat_C",&f);
864: if (f) {
865: (*f)(S,preuse,Sp);
866: } else {
867: MatSchurComplementGetPmat_Basic(S,preuse,Sp);
868: }
869: return(0);
870: }
872: PETSC_EXTERN PetscErrorCode MatCreate_SchurComplement(Mat N)
873: {
874: PetscErrorCode ierr;
875: Mat_SchurComplement *Na;
878: PetscNewLog(N,&Na);
879: N->data = (void*) Na;
881: N->ops->destroy = MatDestroy_SchurComplement;
882: N->ops->getvecs = MatCreateVecs_SchurComplement;
883: N->ops->view = MatView_SchurComplement;
884: N->ops->mult = MatMult_SchurComplement;
885: N->ops->multtranspose = MatMultTranspose_SchurComplement;
886: N->ops->multadd = MatMultAdd_SchurComplement;
887: N->ops->setfromoptions = MatSetFromOptions_SchurComplement;
888: N->assembled = PETSC_FALSE;
889: N->preallocated = PETSC_FALSE;
891: KSPCreate(PetscObjectComm((PetscObject)N),&Na->ksp);
892: PetscObjectChangeTypeName((PetscObject)N,MATSCHURCOMPLEMENT);
893: return(0);
894: }